Double-robust estimators: slightly more Bayesian than meets the eye?

Consider the simple setting of point exposure, outcome and confounding variables, all of which are discrete. As is well known, parametric modeling of outcome given exposure and confounders and also exposure given confounders can yield a double-robust estimator. This has the property of being consistent as long as at least one of the two specified models is correct. Such an estimator can also be cast as arising from a compromise between the parametric outcome model and a nonparametric or saturated outcome model. This brings to mind an alternate compromise based on Bayesian model averaging, and prompts comparisons between the double-robust method and the Bayesian method.